進階搜尋


下載電子全文  
系統識別號 U0026-1906201416070100
論文名稱(中文) 基於不同機率分配下之不合格率管制圖之績效比較
論文名稱(英文) A performance comparison of fraction nonconforming control charts based on different probability distribution perspective
校院名稱 成功大學
系所名稱(中) 工業與資訊管理學系
系所名稱(英) Department of Industrial and Information Management
學年度 102
學期 2
出版年 103
研究生(中文) 劉又慈
研究生(英文) Yu-Tzu Liu
學號 R36011238
學位類別 碩士
語文別 中文
論文頁數 55頁
口試委員 指導教授-張裕清
口試委員-王泰裕
口試委員-蔡青志
中文關鍵字 不合格率管制圖  二項分配累積和/指數加權移動平均管制圖  伯努利分配累積和/指數加權移動平均管制圖  幾何分配累積和/指數加權移動平均管制圖  指數分配累積和/指數加權移動平均管制圖 
英文關鍵字 control chart for fraction nonconforming  binomial CUSUM/ EWMA  Bernoulli CUSUM/ EWMA  geometric CUSUM/ EWMA  exponential CUSUM/ EWMA 
學科別分類
中文摘要 在製造業中,許多製造業的組織在其製程的每個階段中,均會執行產品不合格率之管理,藉由監控產品之不合格率來管制製程良率。因此監控不合格率之管制圖是相當重要之管制工具。除了在製造業中被廣泛的應用,監控不合格率之管制圖在非製造業中的應用,也越來越被重視,例如:服務業、醫療領域等等。而傳統用來監控不合格率之不合格率管制圖(control chart for fraction nonconforming),即p管制圖(p chart),則因存在了許多缺點,如:對於較小之變動偵測效果不佳、當不合格率p很小時,管制圖上將出現許多為零的點等,而後便漸漸發展出了許多其他的新管制方法及管制圖,例如資料轉換法及基於各種不同機率分配之CUSUM/ EWMA管制圖。然而在後續發展出的眾多管制法及管制圖當中,究竟何種方法在何種時機最為適用,並無一明確的使用方針,且過去的比較文獻也僅為某幾個方法在某特定狀況的零星比較,並無一個全面性的比較整合。因此本研究對於各種不同之情形下,各管制圖之績效表現一一做了探討。經由模擬所得之數據結果可發現,在不合格率越低之情況下,指數分配與幾何分配之CUSUM管制圖偵測能力表現差異不大,而以geometric EWMA之表現最佳。此外,隨著不合格率之增加,指數分配之CUSUM、EWMA管制圖都將變得不適用。在p0=0.005~0.2時,geometric EWMA不論在偵測小、大位移時的表現均為所有管制圖當中最好的。而在p0=0.4時,若變動為小、中位移,則geometric EWMA表現最佳。若變動為2倍以上之大位移,則Bernoulli EWMA表現較好。
英文摘要 Control chart for fraction nonconforming has been widely used not only in manufacturing industries but also in non-manufacturing sectors, for example: services, and clinical disciplines, etc. The traditional control chart for fraction nonconforming is p chart, but there are several disadvantages of this chart. Therefore, many other methods for monitoring a fraction have been proposed. However, there is no explicit guideline for choosing the most suitable control chart under a specific condition. In this research, we compare the performance of detecting the increase in p of several control charts based on different probability distributions. We use simulations to compare the detection capability of the control chart. We found that when fraction nonconforming p0 is less than 0.2, geometric EWMA has the best performance. Nevertheless, when p0=0.4, geometric EWMA has the best performance in detecting small change in p, and Bernoulli EWMA is most sensitive in detecting large change in p.
論文目次 摘要 I
英文延伸摘要 II
致謝 VII
表目錄 X
圖目錄 XI
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 4
1.3 研究架構與流程 4
第二章 文獻回顧 6
2.1 管制圖之基本概念與發展概述 6
2.1.1 Shewhart 管制圖 6
2.1.2 CUSUM管制圖 8
2.1.3 EWMA管制圖 9
2.1.4 平均連串長度(Average Run Length, ARL) 10
2.2 監控不合格率之管制圖及管制法 11
2.2.1 p管制圖 12
2.2.2 幾何分配之資料轉換法 14
2.2.3 基於不同分配為基礎之CUSUM管制圖 17
2.2.4 基於不同分配為基礎之EWMA管制圖 21
第三章 研究方法 25
3.1 研究問題描述 25
3.2管制圖之評估指標選擇 27
3.3管制圖之比較方式與設計方法 28
3.4資料模擬的方法 29
3.4.1 伯努利分配計數之ANOS值取得步驟 29
3.4.2 幾何分配計數之ANOS值取得步驟 29
3.4.3 指數分配計數之ANOS值取得步驟 29
第四章 模擬結果與分析 31
4.1管制圖之參數設定 31
4.2管制圖之績效模擬結果 33
4.2.1 高良率製程之管制圖績效模擬 33
4.2.2 不同不合格率下之管制圖績效模擬 34
4.2.3 降低權重對Geometric EWMA管制圖之影響 47
第五章 結論與未來研究建議 50
5.1結論 50
5.2未來研究建議 51
參考文獻 53
參考文獻 Anderson, E. A., & Dian, J. (1996). Using process control chart techniques to analyse crime rates in Houston, Texas. Journal of the Operational Research Society, 47(7).
Bourke, P. D. (1991). Detecting a shift in fraction nonconforming using run-length control charts with 100% inspection. Journal of Quality Technology, 23(3), 225-238.
Bourke, P. D. (2001). The geometric CUSUM chart with sampling inspection for monitoring fraction defective. Journal of Applied Statistics, 28(8), 951-972.
Brook, D., & Evans, D. A. (1972). An approach to the probability distribution of CUSUM run length. Biometrika, 59, 539-549.
Chan, L. Y., Lai, C. D., Xie, M., & Goh, T. N. (2003). A two-stage decision procedure for monitoring processes with low fraction nonconforming. European Journal of Operational Research, 150(2), 420-436.
Chang, T. C., & Gan, F. F. (2001). Cumulative sum charts for high yield processes. Statistica Sinica, 11, 791-805.
Chesher, D., & Burnett, L. (1996). Using Shewhart p control charts of external quality-assurance program data to monitor analytical performance of a clinical chemistry laboratory. Clinical Chemistry, 42(9), 1478-1482.
Crowder, S. V. (1989). Design of exponentially weighted moving average schemes. Journal of Quality Technology, 21, 155-162.
Duran, R. I., & Albin, S. L. (2009). Monitoring a fraction with easy and reliable settings of the false alarm rate. Quality and Reliability Engineering International, 25, 1029-1043.
Evan, W. D. (1963). When and how to use CUSUM charts. Technometrics, 5, 1-22.
Gan, F. F. (1990). Monitoring observations generated from a binomial distribution using modified exponentially weighted moving average control chart. Journal of Statistical Computation and Simulation, 37, 45-60.
Gan, F. F. (1993). An optimal design of CUSUM control charts for binomial counts. Journal of Applied Statistics, 20(4), 445-460.
Gan, F. F. (1994). Design of optimal exponential CUSUM control charts. Journal of Quality Technology, 26(2), 109-124.
Gan, F. F. (1998). Designs of one- and two-sided exponential EWMA charts. Journal of Quality Technology, 30(1), 55-69.
Glushkovsky, E. A. (1994). On-line g-control chart for attribute data. Quality and Reliability Engineering International, 10(3), 217-227.
Goh, T. N. (1987). A control chart for very high yield processes. Quality Assurance, 13, 18-22.
Goh, T. N., & Xie, M. (1994). New approach to quality in a near-zero defect environment. Total Quality Management, 5(3), 3-10.
Goh, T. N., & Xie, M. (2003). Statistical control of a six sigma process. Quality Engineering, 15(4), 587-592.
Green, R. S. (1999). The application of statistical process control to manage global client outcomes in behavioral healthcare. Evaluation and Program Planning, 22, 199-210.
Hawkins, D. M., & Olwell, D. H. (1998). Cumulative Sum Charts and Charting for Quality Improvement: Springer: New York.
Hunter, S. J. (1986). The exponential weighted moving average. Journal of Quality Technology, 18, 203-210.
Johnson, N. L., & Kotz, S. (1970). Distributions in Statistics—Continuous Univariate Distributions: John Wiley & Sons: New York.
Lucas, J. M., & Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: Properties and enhancements. Technometrics, 32, 1-12.
McCool, J. I., & Motley, T. J. (1998). Control charts applicable when the fraction nonconforming is small. Journal of Quality Technology, 30(3), 240-247.
Montgomery, D. C. (2009). Introduction to Statistical Quality Control (6 ed.): Wiley: Hoboken, NJ.
Nelson, L. S. (1994). A control chart for parts-per-million nonconforming items. Journal of Quality Technology, 26(3), 239-240.
Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41, 100-115.
Page, E. S. (1961). Cumulative sum control charts. Technometrics, 3, 1-9.
Pettersson, M. (2004). SPC with applications to churn management. Quality and Reliability Engineering International, 20(5), 397-406.
Pitman, J. (1993). Probability: Springer: New York.
Reynolds, M. R., & Stoumbos, Z. G. (1999). A CUSUM chart for monitoring a proportion when inspecting continuously. Journal of Quality Technology, 31(1), 87-108.
Reynolds, M. R., & Stoumbos, Z. G. (2000). A general approach to modeling CUSUM charts for a proportion. IIE Transactions, 32, 515-535.
Roberts, R. W. (1966). A comparison of some control chart procedures. Technometrics, 8, 411-430.
Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1, 239-250.
Rogerson, P. A. (2006). Formulas for the design of CUSUM quality control charts. Communications in Statistics Theory and Methods, 35(2), 373-383.
Ryan, T. P. (2000). Statistical Methods for Quality Improvement (2 ed.): Wiley: New York, NY.
Ryan, T. P., & Schwertman, N. C. (1997). Optimal limits for attributes control charts. Journal of Quality Technology, 29(1), 86-98.
Szarka, J. L., & Woodall, W. H. (2011). A review and perspective on surveillance of Bernoulli processes. Quality and Reliability Engineering International, 27, 735-752.
Woodall, W. H. (1997). Control charts based on attribute data: Bibliography and review. Journal of Quality Technology, 29(2), 172-183.
Woodall, W. H. (2006). The use of control charts in health-care and public-health surveillance. Journal of Quality Technology, 38(2), 89-104.
Xie, M., Lu, X. S., Goh, T. N., & Chan, L. Y. (1999). A quality monitoring and decision-making scheme for automated production processes. International Journal of Quality and Reliability Management, 16(2), 148-157.
Yeh, A. B., Mcgrath, R. N., Sembower, M. A., & Shen, Q. (2008). EWMA control charts for monitoring high-yield processes based on non-transformed observations. International Journal of Production Research, 46(20), 5679-5699.
李東穎、王復德、陳瑛瑛。(2007)。應用管制圖偵測群突發事件,監控感染率的消長。感染控制雜誌,17(4)。
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2019-07-01起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2019-07-01起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw